In this technical report, we explain how our proposed sparse and low-rank matrix decomposition method for hyperspectral target detection, provided in our work «Automatic Target Detection for Sparse Hyperspectral Images [1]», can be extended to the lq norm (0 < q ≤ 1). Since the use of the l1 norm is still too far away from the ideal l0 norm, many non-convex regularizers, interpolated between the l0 norm and the l1 norm, have been proposed to better approximate the l0 norm.